Neutral-current supernova-neutrino cross sections for ${}^{204,206,208}\mathrm{Pb}$ calculated by Skyrme quasiparticle random-phase approximation

The present work constitutes a detailed study of neutral-current (NC) supernova-neutrino scattering off the stable even-even lead isotopes ${}^{204,206,208}\mathrm{Pb}$. This is a continuation of our previous work [Almosly et al., Phys. Rev. C. 94, 044614 (2016)] where we investigated charged-current processes on the same nuclei. As in the previous work, we have adopted the quasiparticle random-phase approximation (QRPA) as the theory framework and use three different Skyrme interactions to build the involved nuclear wave functions. We test the Skyrme forces by computing the location of the lowest-order isovector spin-multipole giant resonances and comparing with earlier calculations. We have computed the NC cross sections for (anti)neutrino energies up to 100 MeV and estimated the nuclear responses to supernova (anti)neutrinos by folding the obtained cross sections by suitably parametrized Fermi-Dirac distributions of energies of the incoming (anti)neutrinos. We compare our results with results of earlier studies in the case of ${}^{208}\mathrm{Pb}$, which is the only lead isotope where earlier calculations are available.

Figure 1

Distribution of the $M1$ strength (in units of ${\mu }_N^2$) in ${}^{208}\mathrm{Pb}$ for the Skyrme interactions (a) SkX, (b) SkM*, and (c) SLy4.

Figure 2

Total cross sections as functions of the energy of the incoming neutrino for ${}^{208}\mathrm{Pb}$. Kolbe 2001 refers to [31] and Engel 2003 refers to [32].

Figure 3

Contributions from different multipole channels to the total cross section as functions of the energy of the incoming neutrino for the scattering off ${}^{208}\mathrm{Pb}$ using the SkX interaction.

Figure 4

Contributions of the various multipole channels to the cross sections of the neutrino scattering off ${}^{208}\mathrm{Pb}$ for the neutrino energies (a) 15.0 and (b) 95.0 MeV. The interaction SkX has been used in the computations.

Figure 5

Comparison between our averaged cross sections and those of Kolbe 2001 [31] for the neutrino scattering off ${}^{208}\mathrm{Pb}$. Our results are obtained by using the quenching factor ${(1/1.267)}^2$. The horizontal axis displays the $(T,\alpha )$ values used by [31].

Figure 6

Contributions of the different multipole channels to the averaged cross section of the electron-neutrino scattering off ${}^{208}\mathrm{Pb}$. The neutrino-parameter set (I) is used.

Figure 7

Averaged differential cross sections for the electron-neutrino scattering off ${}^{208}\mathrm{Pb}$ as functions of the excitation energy in the final nuclei. The result in (a) is obtained by using the SkX interaction, in (b) by using the ${\mathrm{SkM}}^{*}$ interaction, and in (c) by using the SLy4 interaction.